mckenzie and cara both tried to find the missing side of the right triangle.

mckenzie's cara's work
a2 + b2 = c2 /a2 + b2 = c2
52 + 132 = c2 /52 + b2 = 132
25 + 169 = c2 /25 + b2 = 169
194 = c2 b2 = 144/

13.93 ≈ c b ≈ 12

is either of them correct? explain your reasoning.

It depends on the given information.

McKenzie's work is correct if the two short sides are given as 5 and 13.

Cara's work is correct is almost correct if 5 is one leg, and 13 is the hypotenuse. The exact answer is 12, but she wrote it as approximately equal.  That's her only problem.

By the way, Ddssaa122: when posting questions, the power of a number is written as 5^2 and not 52.   If you copy and paste, please make sure you add the caret sign to indicate a power, or else you will suffer by getting a wrong answer.    5^2=5*5, 52=4*13, so they are not the same.

Ibelieve the answer would be 7, 13, 23